High-Girth Steiner Triple Systems

Abstract: We prove a 1973 conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth. Our proof builds on the method of iterative absorption for the existence of designs by Glock, Kü​hn, Lo, and Osthus while incorporating a "high girth triangle removal process". In particular, we develop techniques to handle triangle-decompositions of polynomially sparse graphs, construct efficient high girth absorbers for Steiner triple systems, and introduce a moments technique to understand the probability our random process includes certain configurations of triples. In this talk we will also give a high-level overview of iterative absorption. This work is joint with Matthew Kwan, Mehtaab Sawhney, and Michael Simkin.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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